iPhone update failed: in recovery mode, Mac spins on "loading ..."
I tried to update my iOS using my Mac and sometime during the night it failed with an "unknown error." It is now in recovery mode ... showing a screen asking for a lightning cable to be inserted. Well, it is, and my Mac sees that an iPhone is attached. But the Mac is spinning on "Software: Loading ..." and it does not appear to be doing anything else. There is no progress-bar. There is no "restore" option or anything else displayed on the Mac screen for this phone.
Does this mean, well, that my Mac is loading software onto the iPhone? Or is it somehow stuck?
Of course the iPhone was first backed-up to the Mac before I started any of this. But the support screens tell me that my Mac should be saying, e.g.: "There is a problem with this iPhone." It isn't doing any of that. So it appears to me to be "stuck" in some way.
iPhone 11, iOS 15